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simplify into a single fraction and write your answer in terms of sin x and cos x: tan x + 1/tan x
 2 years ago
 2 years ago
P>Q Group Title
simplify into a single fraction and write your answer in terms of sin x and cos x: tan x + 1/tan x
 2 years ago
 2 years ago

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ZeHanz Group TitleBest ResponseYou've already chosen the best response.0
Hint: tanx=sinx/cosx, so 1/tanx=cosx/sinx. You now only need to write the sum of these as one fraction!
 2 years ago

P>Q Group TitleBest ResponseYou've already chosen the best response.0
so sin^2x + Cos^2x/cosxsinx ?
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
yes  that is correct but you can simplify this further.\[\sin^2(x)+\cos^2(x)=?\]
 2 years ago

P>Q Group TitleBest ResponseYou've already chosen the best response.0
o um (sinx)(sinx) + (cosx)(cosx)/cosxsinx
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
no, the equation I wrote up there is a well know trig identity  look it up in your notes, you must have been taught this at some stage.
 2 years ago

P>Q Group TitleBest ResponseYou've already chosen the best response.0
Pythagorean trig identity
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
so now make use of that fact to simplify your expression
 2 years ago

P>Q Group TitleBest ResponseYou've already chosen the best response.0
ya idk, I just kinda put it out sin^2x + Cos^2x/cosxsinx = 1 im not seeing how this relates it just made it worse,.
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
the identity you need to use is:\[\sin^2(x)+\cos^2(x)=1\]
 2 years ago

P>Q Group TitleBest ResponseYou've already chosen the best response.0
what do u mean, this has nothing to do with this problem lol I mean all I know is that is the Pythagorean tri identity and that you can move cos or sin and lets say u move sin it goes to the right and u have cos^2(x) = plus or minus radical 1sin^2(x)
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
Look at the steps you took in this problem:\[\begin{align} \tan(x)+\frac{1}{\tan(x)}&=\frac{\sin(x)}{\cos(x)}+\frac{\cos(x)}{\sin(x)}\\ &=\frac{\sin^2(x)+\cos^2(x)}{\cos(x)\sin(x)} \end{align}\]now notice that the numerator contains the terms: \(\sin^2(x)+\cos^2(x)\), and you know that this identity always equals 1. Therefore you can replace \(\sin^2(x)+\cos^2(x)\) by 1.
 2 years ago
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